9.1 telescopes

• Ray diagrams 

  • Magnified or diminished
  • Upright or inverted
  • Real or virtual

  >2F : diminished, inverted, real

  2F : unchanged, inverted, real

  2F > d > F : magnified, inverted, real

  F : no image

  < F : magnified, upright, virtual
• Normal adjustment = when the focal points of the lenses coincide

  Magnification = angle subtended by image at eye / angle subtended by object at unaided eye  

  $M=$$\frac{\theta_i}{\theta_o}$

  Magnification = focal length of objective lens / focal length of eyepiece  

  $M\ =$$\ \frac{F_o}{F_e}$

  $l=$$F_o+$$F_e$

  
• Cassegrain reflecting telescope

  • Parabolic concave primary mirror
  • A gap in the principal axis
  • Convex secondary mirror

  
• Refracting telescope 

  Advantages: 

  • Require less maintenance than reflecting
  • Not as sensitive to temperature changes as reflectors
• Refracting telescope

  Disadvantages: 

  • Scattering and absorption - bubbles and impurities in the glass
  • Difficult and expensive
  • Mirrors easier
  • Large lenses are heavy - distort under its weight
  • Difficult to manoeuvre - have a slower response to astronomical events
  • Need a long focal lens for larger magnification 
  • Can only be mounted and supported around their edges - where they are thinnest and weakest
  • Glass absorbs UV and partial reflection occurs
  • Can only observe visible light
  • Experiences chromatic aberration - can be reduced by adding diverging lens
  • Spherical aberration
• Reflecting telescope

  Advantages:  

  • Can observe greater magnifications
  • Mirrors can be supported from behind
  • Lighter and can respond to astronomical events faster
  • Mirrors don’t experience chromatic aberration

  Disadvantages: 

  • Secondary mirror and support mechanism block incoming light
  • Maintenance - mirrors need to be re-silvered periodically
  • Spherical aberration - if not parabolic, rays won't converge at the same point
  • Objective lens can experience chromatic aberration
• Chromatic aberration

  • Light of different wavelengths refracted to different foci
  • Produce blurred images with coloured edges

  
• Spherical aberration

  • Produces blurred image

  
• Non-optical telescopes

  • Optical telescope - detects wavelengths of light from the visible part of the EM spectrum
  • Non-optical telescope - detects wavelengths of light from other parts of the EM spectrum
  • Radio telescopes
  • Infrared telescopes
  • Ultraviolet telescopes
  • X-ray telescopes
• Ground-based telescopes 

  • Designed to detect a range of wavelengths that span multiple regions of the EM spectrum
  • Operating wavelength range is greatly limited by the absorption of certain wavelengths by the earth's atmosphere
• Space-based telescopes

  • Can detect all wavelengths outside of the Earth's atmosphere
  • Gamma, x-ray, UV
  • All infrared wavelengths split into near-IR, mid-IR, and far-IR

  Advantages:

  • No absorption of EM waves by the atmosphere
  • No light pollution or other sources of interference at ground level
  • No atmospheric effects
  • Scattering or scintillation of light
• Radio telescopes

  • Ground-based
  • Wavelength 1mm-10m
  • Resolution 10-3rad

  Similarities with optical

  • Both use parabolic surfaces to reflect waves
  • Both can be ground-based as the atmosphere is transparent to most radio and optical wavelengths
  • Both used to detect hydrogen emission lines
  • Radio at 21cm; visible at 410, 434, 486, 656cm
• radio telescopes

  Differences from optical 

  • Radio uses single primary reflector / optical uses two mirrors
  • Radio dish doesn't need to be as smooth as optical mirrors
  • Optical must be placed high up and away from cities
  • Radio must be located remotely 
  • Radio waves are not absorbed by dust so used to map the Milky Way / optical waves are absorbed
• Radio telescopes

  Resolving power

  • Radio waves are longer than optical
  • Radio telescopes have lower resolving power
  • Optical telescopes more likely to produce detailed images

  Collecting power 

  • Radio telescopes are larger in diameter
  • Have greater collecting power
  • Radio telescopes more likely to produce brighter images
  • Although many radio sources are weak
• Infrared telescopes

  • Predominantly spaced-based, some ground-based
  • Wavelength 700nm-1mm
  • Resolution 10-6rad (ground)  10-7rad (space)

  Similarities with optical

  • Both constructed using primary concave mirror and secondary convex mirror
  • Many ground-based able to detect optical and near-IR wavelengths as long as positioned away from cities and high above ground
  • Most objects emit visible and IR so information obtainable from both
• Infrared telescopes

  Differences from optical

  • Mirrors in IR must be kept very cold to avoid interference from surrounding heat
  • IR is strongly absorbed by water vapour so must be built in dry high-altitude locations or above the atmosphere
  • Atmosphere is transparent to most optical wavelengths but blocks most IR so space-based is preferable 
  • IR detect warm objects that do not emit visible light such as dust in nebulae and brown dwarfs
• Infrared telescopes

  Resolving power

  • IR telescopes have lower resolving power than optical of the same size due to longer wavelength

  Collecting power

  • Similar for both as the diameters are similar
• Ultraviolet telescopes

  • Space-based
  • Wavelength 10-400nm
  • Resolution 10-7rad

  Similarities with optical

  • Both are constructed using primary concave mirror and secondary convex mirror
  • Many space-based can detect both optical and UV
  • Both used to determine the chemical composition and temperature of objects
  • Many objects emit both so information obtainable from both
• Ultraviolet telescopes

  Differences from optical

  • Mirrors in UV must be smoother than in optical
  • All UV is strongly absorbed by the atmosphere so must be located in space 
  • Space-based UV is inconvenient to maintain
  • UV can detect objects not visible at other wavelengths such as hot gas clouds near stars, supernovae and quasars
• Ultraviolet telescopes

  Resolving power

  • UV telescopes have a higher resolving power than optical of the same size due to shorter wavelength

  Collecting power 

  • Similar as their diameters are similar
• X-ray and gamma telescopes

  • Space-based
  • Wavelength X-rays 0.01-10nm ; gamma <10nm
  • Resolution 10-6rad

  Similarities with optical

  • X-ray and optical use parabolic mirrors to reflect and focus waves
  • All three perform best when positioned in space away from earths atmosphere
  • X-ray and gamma provide additional information about visible objects such as supernova remnants
• X-ray and gamma telescopes

  Differences from optical

  • X-ray telescopes made from a combination of parabolic and hyperbolic mirrors which must be extremely smooth
  • Gamma telescopes don't use mirrors but specialised detectors instead
  • All X-rays and gamma are strongly absorbed by the atmosphere so must be located in space
  • Space-based can be inconvenient to maintain
  • X-ray and gamma can observe non-visible objects and energetic events such as neutron stars, black holes, pulsars and gamma-ray bursts
• X-ray and gamma telescopes

  Resolving power

  • X-ray and gamma have much higher resolving power than optical of the same size due to shorter wavelengths 

  Collecting power 

  • X-ray and gamma are much lower than optical as they have smaller objective diameters
  • X-ray and gamma tend to be extremely bright
• Minimum angular resolution

  • Radians 
  • $\theta\approx\frac{\lambda}{D}$
  • D = diameter of aperture

  Small angular approximation $\sin\theta\approx\theta$

  
• Rayleigh criterion

  • Angular separation and single-slit diffraction through a circular aperture
  • $\theta=$$\frac{s}{d}\ \ \ \ \ \sin\theta=$$\frac{n\lambda}{D}$
  • $\theta$= angular separation (rad)
  • s = distance between two sources
  • d = distance between sources and observer
• Resolving the Rayleigh criterion

  • Resolvable if the centre of one source’s airy disc is at least as far away as the first minimum of the other source
  • Resolvable when $\theta>\frac{\lambda}{D}$
  • Just resolvable when $\theta\approx\frac{\lambda}{D}$
  • Not resolvable when $\theta<\frac{\lambda}{D}$
  • Circular aperture
  • $\theta=$$\frac{1.22\lambda}{D}$
• Resolving power

  Limited by two factors:

  • The Rayleigh criterion
  • Depends on the wavelength of radiation and the diameter of the objective mirror or dish
  • The quality of the detector
  • Limited by the resolution of the detector
  • Number of pixels on a CCD or how fine wire mesh is for an X-ray detector
• Collecting power

  • Proportional to its collecting area
  • $P=$$kd^2$    
  • A bigger dish or mirror collects more energy from an object in a given time
  • Gives a more intense image
  • Can observe fainter objects
• Charged couple devices (CCD)

  • Detector highly sensitive to photons
  • Number of electrons released is proportional to the intensity of the incident light

  Mode of action:

  • Silicon chips are divided into millions of elements (pixels)
  • When light hits, the photoelectric effect releases electrons
  • Trapped in ‘potential well’
  • Builds up charge, measured, image is constructed
• Quantum efficiency = ratio of the number of photons detected to the total photons falling on the device

  • QE = (number of electrons produced per second $\div$ number of photons absorbed per second) x 100
  • Detects 80% of light rays incident on them
  • Eye = 1-4%
  • Film = 4-10%
  • CCD = 70-90%
  • Fewer pixels than the eye
  • Can be made into a digital image
• Resolution

  • The smaller the pixel, the better the resolution 
  • Clearer image
  • $\approx10\mu m$
  • 10x the average human eye
  • Overall resolution of a telescope is limited by the diameter of the objective
  • CCD doesn't affect final image observed
• Convenience

  • Adjustable number of images captured in a time period and exposure time
  • Information stored has remote access
  • Generated images stored and analysed digitally
  • Detect a larger range of wavelengths beyond the visible spectrum
• Comparison to the human eye

  • Much higher QE
  • Can detect much fainter objects
  • Higher resolution
  • Resolution can be increased
  • Better a recording and analysing data